A high accuracy numerical method based on spectral theory of compact operator for biharmonic eigenvalue equations

• Main Author: Zhendong Luo
• Format: Article
• Language: English
• Published: SpringerOpen 2016-02-01
• Series: Journal of Inequalities and Applications
• Subjects: biharmonic eigenvalue equations; spectral-Galerkin discretization; error estimates; spherical domain
• Online Access: http://link.springer.com/article/10.1186/s13660-016-1014-3

Abstract In this study, a high accuracy numerical method based on the spectral theory of compact operator for biharmonic eigenvalue equations on a spherical domain is developed. By employing the orthogonal spherical polynomials approximation and the spectral theory of compact operator, the error estimates of approximate eigenvalues and eigenfunctions are provided. By adopting orthogonal spherical base functions, the discrete model with sparse mass and stiff matrices is established so that it is very efficient for finding the numerical solutions of biharmonic eigenvalue equations on the spherical domain. Some numerical examples are provided to validate the theoretical results.